Question: $ F = \left[\begin{array}{rrr}4 & 1 & 3 \\ -2 & -1 & 1\end{array}\right]$ $ A = \left[\begin{array}{rrr}4 & 1 & -1 \\ -1 & 3 & -2\end{array}\right]$ Is $ F+ A$ defined?
Solution: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ F$ is of dimension $( m \times  n)$ and $ A$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ F$ ) must equal $ p$ (number of rows in $ A$ ) and 2. $ n$ (number of columns in $ F$ ) must equal $ q$ (number of columns in $ A$ Do $ F$ and $ A$ have the same number of rows? Yes Yes No Yes Do $ F$ and $ A$ have the same number of columns? Yes Yes No Yes Since $ F$ has the same dimensions $(2\times3)$ as $ A$ $(2\times3)$, $ F+ A$ is defined.